Proc. SPIE. 10329, Optical Measurement Systems for Industrial Inspection X
KEYWORDS: Mathematical modeling, Interferometry, Monte Carlo methods, Data processing, Signal processing, Nonlinear optics, Signal analysis, Machine learning, Dynamical systems, Electronic filtering, Filtering (signal processing)
The paper deals with the machine learning approach to automatic tuning of extended Kalman filter in application to
interferometric signals processing. The representation of interferometric signals as output of dynamic systems with
varying state vector is presented. It is shown that the challenge of the extended Kalman filter application to
interferometric data processing is selection of initial parameters for the filter. The complex tuning problem is described
in a formal form. The machine learning approach to the automatic filter tuning is proposed. The combination of Monte
Carlo optimization and the gradient descent are implemented for initial filter parameters selection. The optimization
criterion in the form of sum differences between measured and estimated signal value is presented and discussed. The
results of simulated and experimental interferometric signals processing are presented and analyzed. The quality of
amplitude and phase estimation by the automatically tuned filter is at the same level as hand tuned filter. It is shown, that
proposed approach allows to obtain robust results of experimental data processing.
The paper deals with an approach to dynamic parameters estimation of interferometric signals based on non-linear optimization technique. The features of the approach are demonstrated on the example of the gradient descent method as simple iterative non-linear optimization algorithm. The possibilities of using this approach to refine the signal parameters estimates obtained by the extended Kalman filter are considered. The model of one-dimensional interferometric signal is presented. The results of simulated signals processing are analyzed. It was investigated how the quantity of gradient descent iterations influences the quality of parameters estimation. It is shown that the gradient descent provides 65% increase of signal-to-noise ratio for reconstructed signal in comparison with original signal. The proposed method in combination with the extended Kalman filter allows to decrease the amplitude estimation error compared to the unmodified extended Kalman filter. The processing time evaluation results are presented. The recommendations on using proposed approach for interferometric data processing are given.
The application of extended Kalman particle filter for dynamic estimation of interferometric signal parameters is considered. A detail description of the algorithm is given. Proposed algorithm allows obtaining satisfactory estimates of model interferometric signals even in the presence of erroneous information on model signal parameters. It provides twice as high calculation speed in comparison with conventional particle filter by reducing the number of vectors approximating probability density function of signal parameters distribution
The paper deals with the sequential Monte Carlo method applied to the problem of interferometric signals parameters evaluation. A stochastic model of interferometric signal formation is presented. Detailed description of the algorithm is given. The sequential Monte Carlo method modification based on the assumption of Gaussian posterior probability density function of parameters is proposed. The peculiarities of the algorithm and its modification are considered and discussed. The results of parameters evaluation are presented. Data processing rate of proposed methods is estimated and analyzed.